Simplify the following expression: $\dfrac{84y^5}{7y^4}$ You can assume $y \neq 0$.
$ \dfrac{84y^5}{7y^4} = \dfrac{84}{7} \cdot \dfrac{y^5}{y^4} $ To simplify $\frac{84}{7}$ , find the greatest common factor (GCD) of $84$ and $7$ $84 = 2 \cdot 2 \cdot 3 \cdot 7$ $7 = 7$ $ \mbox{GCD}(84, 7) = 7 $ $ \dfrac{84}{7} \cdot \dfrac{y^5}{y^4} = \dfrac{7 \cdot 12}{7 \cdot 1} \cdot \dfrac{y^5}{y^4} $ $\phantom{ \dfrac{84}{7} \cdot \dfrac{5}{4}} = 12 \cdot \dfrac{y^5}{y^4} $ $ \dfrac{y^5}{y^4} = \dfrac{y \cdot y \cdot y \cdot y \cdot y}{y \cdot y \cdot y \cdot y} = y $ $ 12 \cdot y = 12y $